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3 years ago

Find the length of the radius of the following circle. (x + 2)2 + y2 = 10 5 √(10) 100

Mathematics

2 answers:

Makovka662 [10]3 years ago

5 0

For this case we have the following equation:

(x + 2) 2 + y2 = 10

We must remember that the standard equation of the circle is given by:

(x - h) 2 + (y - k) 2 = r2

Where r is the radius.

Therefore, in the given equation the radius is:

r ^ 2 = 10

Clearing we have:

R = root (10)

Answer:

The length of the radius of the circle is:

√ (10)

stepan [7]3 years ago

3 0

Answer:

Find the length of the radius of the following circle.

(x + 2)² + y² = 10

√(10)

Step-by-step explanation:

√(10)

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How many outcome sequences are possible when a die is rolled 4 times where we say for instance that the outcome is 3 4 3 1 if th

STatiana [176]

Answer:

the possible outcome sequences when a die is rolled 4 times is 1296

Step-by-step explanation:

Given the data in the question;

a die is rolled 4 times

and outcomes are { 3, 4, 3, 1 }

we know that; possible number of outcomes on a die is n = 6{ 1,2,3,4,5,6 }

Now when we roll a die lets say, r times

then the total number of possible outcomes will be;

N = $n^r$

given that; r = 4

Hence if we roll a die 4 times;

Total number of possible outcome N = 6⁴

N = 1296

Therefore, the possible outcome sequences when a die is rolled 4 times is 1296

3 0

3 years ago

7. log(x+3)(2x + 3)+log(x+3)(x +5)= 2

OverLord2011 [107]

log(x+3)(2x+3)+log( x+3)( x+5) =2

logx(2x+3)+3(2x+3 )+log x(x+5)+3(x+5)

$log {2x}^{2} + 3x + 6x + 9 + logx {}^{2} + 5x + 3x + 15$

6 0

3 years ago

Diagram 5 shows a right cylinder with a diameter of 2xcm. Given that the total surface area of the cylinder is 96cm³.Find the ma

Paraphin [41]

Given:

The diameter of the right cylinder is 2x cm.

The total surface area is 96 cm cube.

The radius is calculated as,

$\begin{gathered} r=\frac{d}{2} \\ r=\frac{2x}{2} \\ r=x\text{ cm} \end{gathered}$

The total surface area is,

$\begin{gathered} S=2\pi rh+2\pi(r)^2 \\ 96=2\pi xh+2\pi(x^2) \\ h=\frac{96-2\pi(x^2)}{2\pi x} \end{gathered}$

Volume is,

$\begin{gathered} V=\pi(r)^2h \\ =\pi(x^2)\frac{96-2\pi(x^2)}{2\pi x} \\ =\frac{x(96-2\pi(x^2)}{2} \end{gathered}$

Now, differentiate with respect to x,

$\begin{gathered} \frac{dV}{dx}^{}=\frac{d}{dx}(\frac{x(96-2\pi(x^2)}{2}) \\ =\frac{d}{dx}\mleft(x\mleft(-\pi x^2+48\mright)\mright) \\ =\frac{d}{dx}\mleft(x\mright)\mleft(-\pi x^2+48\mright)+\frac{d}{dx}\mleft(-\pi x^2+48\mright)x \\ =1\cdot\mleft(-\pi x^2+48\mright)+\mleft(-2\pi x\mright)x \\ =84-3\pi(x^2)\ldots\ldots\ldots\ldots\text{.}(1) \end{gathered}$

Now,

$\begin{gathered} \frac{dV}{dx}=0 \\ 84-3\pi(x^2)=0 \\ x^2=\frac{16}{\pi} \\ x=\sqrt[]{\frac{16}{\pi}} \end{gathered}$

Now, differentiate (1) with respect to x again,

$\begin{gathered} \frac{d^2V}{dx^2}=\frac{d}{dx}(84-3\pi(x^2)) \\ =-6\pi x \\ At\text{ x=}\sqrt[]{\frac{16}{\pi}} \\ \frac{d^2V}{dx^2}=-6\pi\sqrt[]{\frac{16}{\pi}}$

Since, the double derivative is negative.

$So,\text{ the volume is maximum at }\sqrt[]{\frac{16}{\pi}}$

So, the volume becomes,

$\begin{gathered} V=\pi(x^2)h \\ V=\pi(\sqrt[]{\frac{16}{\pi}})^2h \\ V=\frac{16h}{\pi} \end{gathered}$

Answer: maximum volume of the cylinder is,

6 0

1 year ago

Leslie needs 324 inches of fringe to put around the edge of a tablecloth.The fringe comes in lengths of 10 yards.Of Leslie buys

Delicious77 [7]

324 inches = 27 feet.

10 yards = 30 feet

30 - 27 = 3.

Final answer: 3 feet of fringe will be left over.

P.S, could you mark this the brainly answer? :)

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3 years ago

9x1 + 4x1/100 +7x1/1000 in decimal form

AfilCa [17]

Answer:

9047/1000

Step-by-step explanation:

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3 years ago